Distribution by signature

There is one row for each degree $n$, and the column is indexed by
$r_2$, the number of non-real embeddings, so the signature is
$(n-2r_2, r_2)$. Percentages for individual entries are taken with
the degree. Percentages for the column All give the proportion of
fields of a given degree among all fields in the database.

Distribution by Galois group

For each degree $3\leq n\leq 7$, we give the breakdown of fields in the
database by Galois group. Columns are indexed by
$t$, the $t$-number.
Degrees $1$ and $2$ are omitted because there is only one possible
Galois group for each.
Percentages show the proportions are with respect to the number of fields
in the database of that degree.

Four families of groups have a representative which appears as a Galois
group in every degree $n$, $C_n$, the cyclic group of order $n$, $D_n$, the
dihedral group of order $2n$, $A_n$, the alternating group on $n$ letters,
and $S_n$, the symmetric group on $n$ letters.
Percentages are based on the number of fields in the database of the degree.

Distribution by class number

Class numbers have been computed for 99.98% of
the fields in the database. Some of these
class numbers have been computed under the assumption of the Generalized
Riemann Hypothesis.

For main table entries, the percentage is out of fields of that degree
for which we have computed the class number. For row totals, the percentage
is the number of fields of that degree for which we have computed the class
number divided by the total number of fields of that degree. For column
totals, percentages are based on the total number of fields for which we
have computed the class number. Finally, the lower right corner gives the
percentage of fields in the database for which we have computed the class
number.

Distribution of class number one fields by signature

A number field has class number one if and only if its ring of integers
is a unique factorization domain.

The table below has one row for each degree $n$, and the columns are
indexed by $r_2$, as above.
Percentages for individual entries are with respect
to all fields in the database with that signature for which we have
computed the class number. An entry is not shown if we have not computed
the class number for any fields with that combination of degree and signature.